Amyotrophic Lateral Sclerosis (ALS) is a neurodegenerative disease that affects motor neurons and causes speech and respiratory dysfunctions. Current diagnostic methods are com- plicated, thus motivating the development of an efficient and objective diagnostic aid. We hypothesize that analyses of features capturing the essential characteristics of the biomechanical process of voice production can distinguish ALS patients from non-ALS controls. In this paper, we represent voices with algorithmically estimated vocal fold dynamics from physical models of phonation. To validate our hypothesis, we explore 2 sets of features: simple statistical measurements (Set 1) and phase-space characterizations (Set 2) of estimated vocal fold displacements and range of displacements. Random Forest Classifiers based on Set 1 and Set 2 features yield average AUC-ROC of 99.6% and 82.3%, respectively, in 10-way cross-validation experiments. These results demonstrate the potential of using vocal fold dynamics for detecting ALS from voice recordings.